Details

analyze749.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

sample91.0ms

Algorithm

intervals

Results

22.0ms	51×	body	1280	valid
15.0ms	36×	body	1280	invalid
11.0ms	150×	body	80	valid
11.0ms	36×	body	640	valid
7.0ms	24×	body	640	invalid
4.0ms	19×	body	320	invalid
2.0ms	9×	body	320	valid
2.0ms	13×	body	160	invalid
1.0ms	10×	body	160	valid
1.0ms	16×	body	80	invalid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64` `sqrt-prod_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `insert-posit16`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 97

Calls

3 calls:

5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
14.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series716.0ms

Counts

3 → 9

Calls

3 calls:

172.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
313.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
230.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	370	522
1	370	522
0	12	9
1	12	9
0	370	522
1	370	522
0	12	9
1	12	9
0	1	3
1	1	3
0	529	801
1	529	801
0	11	9
1	11	9
0	529	801
1	529	801
0	11	9
1	11	9
0	1	3
1	1	3
0	233	243
1	233	243
0	8	9
1	8	9
0	233	243
1	233	243
0	8	9
1	8	9
0	1	3
1	1	3

simplify86.0ms

Counts

106 → 106

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5974	2290

prune109.0ms

Filtered

73 candidates to 106 candidates (-45.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	99	7	106
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	99	9	108

Merged error: 0b

Counts

108 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac_binary64`
102×	`sqrt-prod_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
78×	`cbrt-prod_binary64`
58×	`associate-r_binary64`
38×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`associate-r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 205

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
35.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series1.6s

Counts

4 → 12

Calls

4 calls:

434.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
582.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
317.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
312.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	302	387
1	302	387
0	12	15
1	12	15
0	302	387
1	302	387
0	12	15
1	12	15
0	4907	40
1	4907	40
0	302	387
1	302	387
0	12	15
1	12	15
0	302	387
1	302	387
0	12	15
1	12	15
0	4907	40
1	4907	40
0	792	2157
1	792	2157
0	4973	1920
1	4973	1920
0	792	2157
1	792	2157
0	4973	1920
1	4973	1920
0	4920	55
1	4920	55
0	445	1800
1	445	1800
0	19	90
1	19	90
0	445	1800
1	445	1800
0	19	90
1	19	90
0	1193	72
1	1193	72

simplify225.0ms

Counts

217 → 217

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4952	7133
1	4952	7133

prune219.0ms

Filtered

131 candidates to 217 candidates (-65.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	218	8	226

Merged error: 0b

Counts

226 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

195×	`times-frac_binary64`
111×	`add-sqr-sqrt_binary64`
94×	`cbrt-prod_binary64`
91×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
67×	`associate-r_binary64`
47×	`sqrt-prod_binary64`
32×	`add-exp-log_binary64`
22×	`div-inv_binary64`
20×	`add-cbrt-cube_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`associate-/r_binary64` `associate-/l_binary64`
7×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`insert-posit16`
3×	`associate-/l/_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 229

Calls

4 calls:

5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
37.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
17.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
13.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series1.5s

Counts

4 → 12

Calls

4 calls:

173.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
433.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
603.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
290.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	400	1845
1	400	1845
0	14	9
1	14	9
0	400	1845
1	400	1845
0	14	9
1	14	9
0	1	3
1	1	3
0	529	1908
1	529	1908
0	4837	1464
1	4837	1464
0	529	1908
1	529	1908
0	4837	1464
1	4837	1464
0	4759	9
1	4759	9
0	698	1971
1	698	1971
0	23	9
1	23	9
0	698	1971
1	698	1971
0	23	9
1	23	9
0	1	3
1	1	3
0	233	243
1	233	243
0	8	9
1	8	9
0	233	243
1	233	243
0	8	9
1	8	9
0	1	3
1	1	3

simplify152.0ms

Counts

241 → 241

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5187	7957

prune302.0ms

Filtered

178 candidates to 241 candidates (-35.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	241	8	249

Merged error: 0b

Counts

249 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
5.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod_binary64`
91×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
61×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
40×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`unswap-sqr_binary64` `sqrt-div_binary64`
8×	`pow1_binary64`
6×	`associate-/r_binary64` `associate-l_binary64` `associate-/l_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 172

Calls

4 calls:

27.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

378.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
262.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
312.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
316.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	302	387
1	302	387
0	12	15
1	12	15
0	302	387
1	302	387
0	12	15
1	12	15
0	4907	40
1	4907	40
0	302	387
1	302	387
0	12	15
1	12	15
0	302	387
1	302	387
0	12	15
1	12	15
0	4907	40
1	4907	40
0	436	672
1	436	672
0	32	126
1	32	126
0	436	672
1	436	672
0	32	126
1	32	126
0	109	85
1	109	85
0	525	1316
1	525	1316
0	69	456
1	69	456
0	525	1316
1	525	1316
0	69	456
1	69	456
0	139	3
1	139	3

simplify65.0ms

Counts

184 → 184

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	364	5359
1	364	5359

prune129.0ms

Filtered

116 candidates to 184 candidates (-58.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	184	8	192

Merged error: 0b

Counts

192 → 8

regimes162.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	52
1	20	52

end0.0ms

sample2.8s

Algorithm

intervals

Results

615.0ms	1373×	body	1280	valid
495.0ms	1123×	body	1280	invalid
358.0ms	1184×	body	640	valid
341.0ms	4646×	body	80	valid
295.0ms	962×	body	640	invalid
111.0ms	515×	body	320	valid
108.0ms	506×	body	320	invalid
42.0ms	282×	body	160	valid
41.0ms	522×	body	80	invalid
38.0ms	257×	body	160	invalid

Iter	Nodes	Cost
0	370	522
1	370	522
0	12	9
1	12	9
0	370	522
1	370	522
0	12	9
1	12	9
0	1	3
1	1	3
0	529	801
1	529	801
0	11	9
1	11	9
0	529	801
1	529	801
0	11	9
1	11	9
0	1	3
1	1	3
0	233	243
1	233	243
0	8	9
1	8	9
0	233	243
1	233	243
0	8	9
1	8	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	370	522
1	370	522
0	12	9
1	12	9
0	370	522
1	370	522
0	12	9
1	12	9
0	1	3
1	1	3
0	529	801
1	529	801
0	11	9
1	11	9
0	529	801
1	529	801
0	11	9
1	11	9
0	1	3
1	1	3
0	233	243
1	233	243
0	8	9
1	8	9
0	233	243
1	233	243
0	8	9
1	8	9
0	1	3
1	1	3

Details

analyze749.0ms

sample91.0ms

simplify27.0ms

prune5.0ms

localize10.0ms

rewrite33.0ms

series716.0ms

simplify86.0ms

prune109.0ms

localize16.0ms

rewrite72.0ms

series1.6s

simplify225.0ms

prune219.0ms

localize14.0ms

rewrite89.0ms

series1.5s

simplify152.0ms

prune302.0ms

localize13.0ms

rewrite56.0ms

series1.3s

simplify65.0ms

prune129.0ms

regimes162.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample2.8s

Profiling

Iter	Nodes	Cost
0	370	522
1	370	522
0	12	9
1	12	9
0	370	522
1	370	522
0	12	9
1	12	9
0	1	3
1	1	3
0	529	801
1	529	801
0	11	9
1	11	9
0	529	801
1	529	801
0	11	9
1	11	9
0	1	3
1	1	3
0	233	243
1	233	243
0	8	9
1	8	9
0	233	243
1	233	243
0	8	9
1	8	9
0	1	3
1	1	3